Remark The net result of imposing this constraint is that the particles are guided by the gradient of the drift potential, and as such, \(\phi (x)\)  plays the role of a pilot wave, similar in spirit to that of Bohmian mechanics. Eventually \(\phi (x)\)  will be responsible for many quintessential quantum phenomenon, such as entanglement and interference. A recent improvement in ED [1]} has been to recognize that the introduction of such a function is not as ad hoc as it might, nevertheless, first appear. Note that in the ED we develop here there are two important pairings. The first pertains to the entropic origins of ED, and consists of probabilities and their constraints. Another important pairing occurs when we adopt a Hamiltonian formalism to update the evolving constraints. It is here that we must introduce a canonical coordinate, the probability \(\rho (x)\) , and its conjugate momentum. In an ED driven by constraints and by Hamiltonians it is therefore exceedingly natural that the two pairings may have some intimate connection. This is accomplished by assigning to the drift potential \(\phi (x)\)  a dual role, first as encoding the information in the form of constraints, and second, by identifying it as the momentum conjugate to \(\rho (x)\) .

